Questions: Question 1, 8.8.1 HW Score: 45%, Part 2 of 4 Points: 0 of 1 The credit card with the transactions described on the right uses the average daily balance method to calculate interest. The monthly interest rate is 1.5% of the average daily balance. Calculate parts a-d using the statement on the right. Transaction Description Transaction Amount ------ Previous balance, 6210.00 March 1 Billing date March 5 Payment 350.00 credit March 7 Charge: Restaurant 30.00 March 12 Charge: Groceries 80.00 March 21 Charge: Car Repairs 280.00 March 31 End of billing period Payment Due Date: April 9 a. Find the average daily balance for the billing period. Round to the nearest cent. The average daily balance for the billing period is 6080.32. (Round to the nearest cent as needed.) b. Find the interest to be paid on April 1, the next billing date. Round to the nearest cent. The interest to be paid on April 1 is . (Use the answer from part a to find this answer. Round to the nearest cent as needed.)

Solution Steps

To solve this problem, we need to follow these steps:

1. Calculate the average daily balance for the billing period.
2. Use the average daily balance to calculate the interest to be paid on the next billing date.

1. Average Daily Balance Calculation:

   • Determine the balance for each day of the billing period.
   • Sum the daily balances.
   • Divide the total by the number of days in the billing period.

2. Interest Calculation:

   • Multiply the average daily balance by the monthly interest rate.

We begin with the previous balance of \( \$6210.00 \) on March 1. The transactions are as follows:

• From March 1 to March 5 (4 days), the balance remains \( \$6210.00 \).
• On March 5, a payment of \( \$350.00 \) is made, resulting in a new balance of \( 6210 - 350 = 5860.00 \).
• From March 5 to March 7 (2 days), the balance is \( \$5860.00 \).
• On March 7, a charge of \( \$30.00 \) is made, resulting in a new balance of \( 5860 + 30 = 5890.00 \).
• From March 7 to March 12 (5 days), the balance is \( \$5890.00 \).
• On March 12, a charge of \( \$80.00 \) is made, resulting in a new balance of \( 5890 + 80 = 5970.00 \).
• From March 12 to March 21 (9 days), the balance is \( \$5970.00 \).
• On March 21, a charge of \( \$280.00 \) is made, resulting in a new balance of \( 5970 + 280 = 6250.00 \).
• From March 21 to March 31 (10 days), the balance is \( \$6250.00 \).

The average daily balance is calculated by summing the daily balances and dividing by the total number of days in the billing period (31 days):

\[ \text{Average Daily Balance} = \frac{(4 \times 6210) + (2 \times 5860) + (5 \times 5890) + (9 \times 5970) + (10 \times 6250)}{31} \]

Calculating this gives:

\[ \text{Average Daily Balance} = \frac{24840 + 11720 + 29450 + 53730 + 62500}{31} = \frac{182740}{31} \approx 6074.67 \]

The interest to be paid on April 1 is calculated using the average daily balance and the monthly interest rate of \( 1.5\% \) (or \( 0.015 \)):

\[ \text{Interest} = \text{Average Daily Balance} \times \text{Monthly Interest Rate} = 6074.67 \times 0.015 \approx 91.12 \]

Final Answer